Integrals

**qzno** · January 29th 2009, 11:23 AM

find the following indefinite integral (using u substitution):

$\int x \sqrt[3]{x+1} dx$

evaluate the following definite integrals using the Fundamental Theorem of the Calculus (u sub involved):

$\int_{0}^{\frac{\pi}{4}} (1 + tan^2 x)sec^2 x dx$

$\int_{0}^{2|b|} \frac{x}{\sqrt{x^2 + b^2}} dx$

**chabmgph** · January 29th 2009, 11:30 AM

Originally Posted by qzno

find the following indefinite integral (using u substitution):

$\int x \sqrt[3]{x+1} dx$

evaluate the following definite integrals using the Fundamental Theorem of the Calculus (u sub involved):

$\int_{0}^{\frac{\pi}{4}} (1 + tan^2 x)sec^2 x dx$

$\int_{0}^{2|b|} \frac{x}{\sqrt{x^2 + b^2}} dx$

1) Let $u=x+1$

2) Let $u=\tan x$

3) Let $u=x^2+b^2$

**qzno** · January 29th 2009, 11:32 AM

I already tried this for them all haha

**qzno** · January 29th 2009, 12:17 PM

for the second one I got the evaluated answer to be:

$\frac{(tan 1)^3}{3}$

is this correct?

and i still cant do the last question : (
thanks to anyone who helps!!

**qzno** · January 29th 2009, 04:37 PM

For the first one when i let u = x + 1, i got the answer to be: $\frac{3x(x+1)^{\frac{4}{3}}}{4} + c$
is this correct?

i still havnt figured out the third one : (

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